Enter your search into one or more of the boxes below:
You can refine your search by selecting from any of the options below:
An Introduction to Convex Polytopes

An Introduction to Convex Polytopes (Paperback)

Printed to order. Despatched in 2-3 weeks.
Email me when back in stock


The aim of this book is to introduce the reader to the fascinating world of convex polytopes. The highlights of the book are three main theorems in the combinatorial theory of convex polytopes, known as the Dehn-Sommerville Relations, the Upper Bound Theorem and the Lower Bound Theorem. All the background information on convex sets and convex polytopes which is m~eded to under- stand and appreciate these three theorems is developed in detail. This background material also forms a basis for studying other aspects of polytope theory. The Dehn-Sommerville Relations are classical, whereas the proofs of the Upper Bound Theorem and the Lower Bound Theorem are of more recent date: they were found in the early 1970's by P. McMullen and D. Barnette, respectively. A famous conjecture of P. McMullen on the charac- terization off-vectors of simplicial or simple polytopes dates from the same period; the book ends with a brief discussion of this conjecture and some of its relations to the Dehn-Sommerville Relations, the Upper Bound Theorem and the Lower Bound Theorem. However, the recent proofs that McMullen's conditions are both sufficient (L. J. Billera and C. W. Lee, 1980) and necessary (R. P. Stanley, 1980) go beyond the scope of the book. Prerequisites for reading the book are modest: standard linear algebra and elementary point set topology in [R1d will suffice.

Science & MathematicsMathematicsCombinatorics & graph theory Publisher: Springer-Verlag New York Inc. Publication Date: 30/09/2012 ISBN-13: 9781461270232  Details: Type: Paperback Format: Books
Availability: Printed to order. Despatched in 2-3 weeks.  

More books by Arne Brondsted

Leave Review


Delivery Options

All delivery times quoted are the average, and cannot be guaranteed. These should be added to the availability message time, to determine when the goods will arrive. During checkout we will give you a cumulative estimated date for delivery.

Location 1st Book Each additional book Average Delivery Time
UK Second Class Available free for ALL orders. No charge for each additional book. 3-7 Days
UK First Class £4.50 £1.00 1-2 Days
UK Courier £7.00 £1.00 1-2 Days
Western Europe** Courier £17.00 £3.00 2-3 Days
Western Europe** Airmail £5.00 £1.50 4-14 Days
USA / Canada Courier £20.00 £3.00 2-4 Days
USA / Canada Airmail £7.00 £3.00 4-14 Days
Rest of World Courier £22.50 £3.00 3-6 Days
Rest of World Airmail £8.00 £3.00 7-21 Days

** Includes Austria, Belgium, Denmark, France, Germany, Greece, Iceland, Irish Republic, Italy, Luxembourg, Netherlands, Portugal, Spain, Sweden and Switzerland.

Delivery Help & FAQs

Returns Information

If you are not completely satisfied with your purchase*, you may return it to us in its original condition with in 30 days of receiving your delivery or collection notification email for a refund. Except for damaged items or delivery issues the cost of return postage is borne by the buyer. Your statutory rights are not affected.

* For Exclusions and terms on damaged or delivery issues see Returns Help & FAQs

You might also like

Descriptive Complexity, Canonisation,...
Martin Grohe
Nicholas Loehr
Introduction to Computational Social...
Claudio Cioffi-Revilla
Graph Theory
Reinhard Diestel
Latest Blog
Read an Extract from A Skinful of Shadows

Read an extract from the eagerly awaited new novel by the Costa-winning Frances Hardinge, A Skinful of Shadows.

#FoylesFive: Elsewhere-Elsewhen

Jen from the Web Team shares a selection of books that will transport the reader to another time and place.

Growler: The Inspiration for the Now Iconic Bear

James Campbell describes how the groundbreaking approach to illustration adopted by Milne and Shepard came about, which bear provided the inspiration for the drawings and which of the characters was Shepard's secret favourite.

View all Blog Entries
Show/Hide Tweets
© W&G Foyle Ltd